The magnetic dipole moment (MDM) of a particle is its fundamental characteristic that determines the torque which particle experiences in an external magnetic field. The MDMs of many particles are presently known [1]}.
For electron the QED prediction agrees with experimentally measured value up to very high precision.
For muon the measurement of the BNL E821 experiment [2]} disagrees with the Standard Model prediction by 3–4 standard deviations, which may suggest physics beyond the Standard Model.
The disagreement for the muon \(g-2\)  is the subject of many studies (see, e.g., review [3]}). The MDM of the \(\tau \) -lepton has not been measured so far and is of great interest for testing calculations in the Standard Model [4]}.
